The 48-year-old has experience of working in sports marketing and the leisure industry as well as in cricket administration with four counties.
He has been assistant secretary at Essex, secretary at Gloucestershire and chief executive at Leicestershire. He has spent the last four years at Trent Bridge.
As a former international hockey umpire, he also had recent success in creating a rescue package as financial adviser and vice-president to the English Hockey Association.
Lamb, who held the post for six years, completed his period in office earlier this month after initially announcing his resignation in May.
ECB chairman David Morgan revealed Collier's business background had helped him land the job.
"We were looking for someone with a strong business background coupled with a knowledge and love of cricket," he said.
"David has both qualities. He has successfully led Nottinghamshire for the past five years and also has significant business experience both within and outside of cricket."
Collier said: "I am delighted to have been offered the opportunity to lead the ECB at such an exciting point in the game's history.
"During the past year the success of the England team, the increasing crowds at Twenty20 cricket, the development of young cricket to the Academy system at both county and national level and the expansion of cricket being played at club and school level demonstrates that there are solid foundations for the future of cricket in England and Wales."
Lamb left after seven years over his handling of the crisis over whether England should play in Zimbabwe.
Lamb, 51, had also been at odds with chairmen of the English counties over proposals to restructure the domestic game from 2006.